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amit's school is an unusual school.it has 1677 students in grades 3-6.There are twice as many fifth graders as sixth graders and three times as many forth graders as fifth graders. Finally, there are five times as many third graders as fourth graders. How many fifth graders are in Amit's school?​

Respuesta :

calculista

Answer:

[tex]86\ fifth\ graders[/tex]

Step-by-step explanation:

Let

x-----> number of students in third grade

y----> number of students in  fourth grade

z---> number of students in  fifth grade

r----> number of students in  sixth  grade

we know that

[tex]x+y+z+r=1,677[/tex] -----> equation A

[tex]z=2r[/tex]  ----> [tex]r=0.5z[/tex] -----> equation B

[tex]y=3z[/tex] -----> equation C

[tex]x=5y[/tex] ----> equation D

Substitute equation C in equation D

[tex]x=5(3z)=15z[/tex] -----> equation E

Substitute equation B, equation C, equation E in equation A and solve for z

[tex](15z)+(3z)+z+(0.5z)=1,677[/tex]

[tex]19.5z=1,677[/tex]

[tex]z=1,677/19.5=86\ fifth\ graders[/tex]

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